The mechanical properties of supergraphene, cyclicgraphene and graphyne are studied using molecular dynamics simulations based on the AIREBO potential. In particular, we present the chirality-dependence of their mechanical properties, including Young's moduli, shear moduli, Poisson's ratios, ultimate strength and ultimate strains. The relationship of their Young moduli, shear moduli and Poisson ratios is in the order of Y(su) (super) < Y(cy) (cyclic) < Y(gy) (graphyne) < Y(ge) (graphene), G(su) < G(cy) < G(gy) < G(ge) and v(su) > v(cy) > v(gy) > v(ge) in corresponding zigzag and armchair sheets, respectively. Their intersheet adhesion energy is obtained as γ(su) = 30, γ(cy) = 99 and γ(gy) = 149 mJ m(-2), which are much lower than that of γ(ge) = 291 mJ m(-2) (the value is in good agreement with the latest experimental result γ(ge) = 310 ± 30 mJ m(-2)). The obtained adhesion energy is accurately characterized by continuum modeling of the van der Waals interactions. Our study is very useful for the future applications of graphene-like materials in nanoelectromechanical systems.